In an open letter to The Post, the spitting-mad boss of the Patrolmen’s Benevolent Association ripped his teachers-union counterpart Saturday for the “disgraceful” decision to co-sponsor the Rev. Al Sharpton’s anti-police rally next week.

PBA President Pat Lynch fired both barrels at United Federation of Teachers President Michael Mulgrew, saying, “It is absolutely ridiculous that [Mulgrew] . . . would waste his members’ dues to get involved with a march that has nothing to do with teachers or his union.

“Mulgrew knows that the UFT is under siege from all sides, and this is purely an attempt to distract attention from that mounting criticism,” Lynch wrote, referring to the union’s chronic battles over teacher tenure and charter schools as well as the “substandard” contract Mulgrew recently negotiated for his membership.

“How would he like it if police officers lined up with the activists who oppose his efforts to shield bad teachers and undermine effective charter schools?” Lynch fumed.

In a series of personal jabs, Lynch suggested Mulgrew was more concerned with “continuing to curry favor with politicians and Al Sharpton” than in helping his 200,000 union members or the city’s 1.1 million schoolchildren.

Labor insiders were shocked by the escalating battle between the two political heavyweights who head two of the city’s most powerful unions.

“It’s just not right,” said Bill Pelletier, former VP for the Transit Workers Union. “For the leaders to get involved with this is out of character.”

He said such disputes are usually resolved privately at the Central Labor Council.

It is absolutely ridiculous that [Mulgrew] . . . would waste his members’ dues to get involved with a march that has nothing to do with teachers or his union.

- Pat Lynch

The Queens-born Lynch, 51, in a phone interview that followed his literary fusillade, said he was blindsided by Staten Islander Mulgrew, 49.

“We’ve never had a problem,” said Lynch, who represents 50,000 cops. “We’re amazed that he would chime in on an issue like this.

“We typically boost each other up. I’m dumbfounded why Mike Mulgrew would do and say the things that he has,” Lynch told The Post. “It’s disgraceful.”

Detectives’ Endowment Association President Michael Palladino said he was “not surprised” by Mulgrew’s co-sponsorship.

“Teachers union leadership marched alongside Sharpton, with the Bloods and Crypts, during the Bell case,” Palladino said. “I imagine most educators would be embarrassed by Mulgrew’s actions.”

The UFT declined to comment.

On Friday, Mulgrew said, “Mr. [Eric] Garner’s death was a tragedy for the city. Teachers want to help ensure that something like this doesn’t happen again.”

The teachers union is one of four sponsors of the planned Aug. 23 protest in Staten Island.

A flier for the march, which was attached to a UFT e-mail to its members, bills it as a “March for Justice for Victims of Police Brutality” and adds, “We Will Not Go Back.”

The union has also offered to provide protesters rides.

The family of Garner, the 43-year-old Staten Islander who died after an NYPD officer put him in a chokehold while trying to arrest him for selling untaxed cigarettes, is expected to lead the march with Sharpton.

Protesters will take cars and buses over the Verrazano-Narrows Bridge, then march between the Tompkinsville corner where Garner died and the Staten Island district attorney’s office a half-mile away.

Other sponsors of the protest include the NAACP and SEIU Local 1199, the powerful health-care workers union that is allied with de Blasio.